The National Catholic Reporter reported Thursday it appears church officials in Rome are ready to accept Rigali's resignation and a source said a news conference could be expected early this week.
The Philadelphia Inquirer reported Monday it appeared Rigali would be succeeded by Denver Archbishop Charles J. Chaput. The newspaper said its sources say Rigali will hold a news conference Tuesday to announce Pope Benedict XVI will name Chaput, 66, to the Philadelphia post.
Chaput has led the Denver archdiocese since 1997.
The 1.5 million-member Philadelphia archdiocese has been rocked by the Catholic Church's clergy sex scandal. Rigali suspended 29 clerics in March, the month after a grand jury report on allegedly predatory clergy in the archdiocese.
The Reporter said a chancery official said the situation in Philadelphia is like "quicksand … . Everything feels like it is sinking."
Rigali, 76, a Los Angeles native, marked his eighth year as a cardinal Saturday. Before taking over the Philadelphia archdiocese, he was archbishop in St. Louis.